Pointwise multipliers for Campanato spaces on Gauss measure spaces

Abstract

In this paper, the authors characterize pointwise multipliers for Campanato spaces on the Gauss measure space $({\mathbb{R}}^n,|\cdot |,\gamma )$, which includes $BMO\left(\gamma \right)$ as a special case. As applications, several examples of the pointwise multipliers are given. Also, the authors give an example of a nonnegative function in $BMO\left(\gamma \right)$ but not in $BLO\left(\gamma \right)$.